Education ∪ Math ∪ Technology

Tag: The Reflective Educator (page 23 of 43)

Joining the CFHE12 MOOC

I’ve decided to participate a MOOC on the future of higher education. The MOOC is being faciliated by George Siemens and Rory McGreal, and seems like it will be a vastly different experience than the MOOC on Mathematical Thinking I’m currently exploring being run by Keith Devlin. My primary objective will be to explore the difference in format between these two MOOCs and see which of them I think is a more productive learning environment, specifically focused on the needs of my students.

Hopefully I’ll also get a chance to meet some people who are involved in coordinating these types of learning experiences for their universities.

Testing new Captcha system

So I have quite a bit of spam which is posted to my site, probably between 50 and 100 comments a day at least. I’ve been using some heavy handed spam filters to try and curb it, but these filters have probably blocked legitimate comments, which kind of defeats the purpose of having a blog. One solution is to use a Captcha instead of a spam filter, but these are generally easy to circumvent with a bit of programming to defeat the Captcha. What I’ve done is created my own unique Captcha system, which is probably not worth the effort for anyone to crack (given that I have only 1 site using the Captcha so the reward for solving it is minimal). This should block spam computer programs from posting comments to my blog, and so I’ve (at least temporarily) disabled the anti-spam filters.

The solution is unfortunately not accessible. I will look into a way of providing an audio file replacement in case anyone who is visually impaired is reading my blog and wants to comment. For now, if that is the case, please feel free to use the contact link above.

Could you please test that this Captcha works for me? I want to verify that I have not accidentally made it impossible for anyone to comment.

Update:

It seems that my Captcha works. I’ve received only 3 spam since I implemented it, all of which could have easily been entered by a human being. Comparing this to the hundreds and hundreds of spam I used to receive in the same time period makes me happy. Hopefully this mean that it will be also easier for actual human beings to comment on my blog.

Here’s 3 minutes of my website log. Almost all of the rest of my log is filled with similar mesages, so I’m encouraged by the success of my Captcha module. Some spam has gotten through, but so far it seems that it is either infrequent, or I can block the spammer by IP address.

Captcha log

Leadership 2.0 chat

George Couros has set up a series of speakers on the general topic of leadership in schools in the 21st century. Starting today, and for each of the following nine weeks, George will be facilitating presentations from exceptional leaders from across North Ameria. You can read more about his initative on his blog.

To help extend this conversation, George asked me to moderate a Twitter discussion on the same or related topics on the Thursday following the webinars. The first discussion is happening this Thursday at 7pm PST and our first discussion topic is, "What does leadership 2.0 mean?" The hashtag for the discussion is #leadership20 if you want to follow along.

Please share this discussion series with any educational administrators you know (or any aspiring educational leaders). Anyone who has an interest in educational leadership is welcome to attend the discussion.

Copyright in Canada

Introduction

My colleague and I presented last night to the rest of our colleagues about copyright. We spoke about the state of copyright in Canada, and what implications this has on our classroom teaching & learning. This is the presentation we used. Unfortunately, an article by Larry Kuehn suggested to us that some of what we shared was in fact no longer true. Not wanting to present an incomplete or inaccurate picture to our colleagues, we did some further research.

The first thing we discovered is that Larry Kuehn’s article refers mostly to the impact of Bill C-11, which is not currently in effect (it has yet to be formally passed as a law), which means that although we will have to give another presentation on copyright when the bill comes into effect, our presentation yesterday was still substantially true.

What follows is my interpretation of current and future copyright law, and should not be considered an expert opinion on this matter.

 

Current Copyright

During the process of our research, we discovered that there are a number of Supreme Court of Canada rulings that do impact education in Canada in the current environment. The Supreme Court of Canada rulings, according to Contact North, operate under three principles:

  1. An Unequivocal Endorsement of Users’ Rights
  2. Technological Neutrality as a Foundational Principle of Copyright Law
  3. Expansion of Fair Dealing

The first principle means that the Supreme Court assumes that users’ rights in terms of copyright use are important and foundational to determining, when there is an apparent conflict between user and copyright holder rights, what right the user has to copy and access copyrighted material. 

The second principle re-enforces the idea in current copyright law that copyright should be technology neutral. For example, it is currently not permitted to scan a textbook, and then share that material in an online environment, even when such sharing is of a limited portion of the entire textbook, but it is considered permissible to share the same exact work by photocopying and handing it out. This ruling suggests that if sharing a portion of work is acceptable in one format, it must be acceptable in all formats.

During my MET degree at UBC, we were required to purchase paper copies of the research and articles our professors wanted to share with us, even though the entire program was online. I thought this was kind of ridiculous, but it turned out that UBC was, at the time, required to purchase a separate license for sharing work in a different medium than a photocopy. Now, if my interpretation of this principle is accurate (the recent Access Copyright ruling will also assist in this respect), UBC should feel free to share their educational research in whatever format is most appropriate for them.

The third principle expands the possible uses of fair dealing. For example, the rulings from the Supreme Court indicate that "private study" could include study with a teacher. In particular, "[t]he word “private” in “private study” should not be understood as requiring users to view copyrighted works in isolation." (Alberta (Education) v. Canadian Copyright Licensing Agency , Supreme Court of Canada, July 12th, 2012). Teachers can now make copies of work under fair dealing for the purpose of assisting their students with their private study, provided they are only providing short excerpts of that work, and they are not required to pay any fee to Access Copyright for this right.

 

Future copyright law

Bill C-11 appears to significantly expand user rights for copyrighted material, in many of the same ways such access has been improved for users of copyrighted material in the United States.

The non-commercial user generated content section of the law, for example, makes it explicitly clear that users have a right to use copyrighted material in their own creations provided such creations are: not for commercial purposes, they cite their source of material clearly, the work they are copying is itself not in violation of copyright, and the work created does not substantially harm the commercial rights of a copyrighted work. This will mean that students will be free to use copyrighted material in their projects (provided they cite their work appropriately), since it should be clear that no student work is likely to harm the commercial interests of a copyright holder’s work.

A further benefit of the law is that it distinguishes between damages for violations of copyright for commercial and non-commercial purposes. Basically, the penalties for copyright violation are greatly reduced for violates that result in non-commercial uses of copyrighted material.

It also adds some limitations for copyrighted material that may be quite difficult for educational instutions to manage. For example, if a student has received copyrighted course material in a course delivered via telecommunications technology (ie, any online course), educational instutions are expected to delete such work within 30 days of the end of the course, as defined by the date students received their end of course evaluations. This could end up be quite cumbersome for teachers, especially teachers who teach the same, or essentially the same, course many years in a row.

 

What is not addressed

Lawrence Lessig makes an excellent argument for an even greater expansion of user rights for copyrighted material, and Bill C-11 does not go as far as his vision of reformed copyright law. The digital rights management clause of Bill C-11 is problematic, as it almost certainly guarantees that we will continue to see the rise of digital rights management (DRM) materials, as the law allows for modification of work which has no DRM, and no modification of work with DRM included.

The law does not recognize that ideas themselves are often not generated in isolation, and that allowing for copyright on one portion of a work means that whomever gets to the copyright office first with a trademark, patent, or copyright request will hold copyright on ideas that may in fact be the culimation of many people’s work. Stephen Johnson describes how ideas are usually formed in networks, and that it can be difficult to attribute an idea to a specific individual. Copyright law still assumes this is not the case – that ideas are somehow formed in this magical ether separate from the rest of humanity. As Sir Isaac Newton observed, "If I have seen further it is by standing on ye sholders of Giants [sic]."

Copyright law is generally biased toward people with the resources to fight for their copyright, and to promote their work over others. The new copyright law does not significantly address this inequality. We have situations around the world where companies are bought and sold because of the patents they hold, since the potential intellectual property rights of those patents is huge, regardless of whether those patents actually ever get used. We have potentially thousands of devices which could improve human existence which will never be created because they aren’t cost effective for the companies that hold the patent, and for which the patents are too expensive for small developers to afford.

 

References:

Alberta (Education) v. Canadian Copyright Licensing Agency (Access Copyright), 2012 SCC 37

Re:Sound v. Motion Picture Theatre Associations of Canada, 2012 SCC 38

Rogers Communications Inc. v. Society of Composers, Authors and Music Publishers of Canada, 2012 SCC 35

Entertainment Software Association v. Society of Composers, Authors and Music Publishers of Canada, 2012 SCC 34

Society of Composers, Authors and Music Publishers of Canada v. Bell Canada, 2012 SCC 36

Bill C-11, "An Act to Amend the Copyright Act", retrieved September 27th, 2012

Contact North, "The Perfect Storm: Canadian Copyright Law 2012", retrieved September 27th, 2012

Michael Geist, "Beyond Users’ Rights: Supreme Court Entrenches Technological Neutrality as a New Copyright Principle", retrieved September 27th, 2012

Larry Kueh, "Education is the big winner in copyright changes", retrieved September 27th, 2012

Talks that inspire change in schools

I was recently asked to share some talks which might inspire parents who have come from a traditional schooling system to think differently about how schools should be operated. Here is my list (please feel free to add your own in the comments below as I am sure I have missed some gems out there).

KT Pirquet on Homework in Math

The following was shared to me and I felt it deserved a wider audience, so with permission of the author, I am sharing it here. The author has asked me to point out that this writing is copyrighted by her, and that permission is required from her if you wish to copy it or publish it in another format. You can contact me through the contact link above if you want to get in touch with the author.

 

 

Ah, yes, homework.

To mark it? To leverage the pressure by counting the marks in the final average? Perchance not to assign it at all?  Why can’t we seem to settle this, or at least find a way to get students to do their homework without all this agony?  I believe we have met the enemy, and he looks familiar.

It is partly the system and partly ourselves creating this culture that teaches students in a perverse and relentless way to view the whole school experience as oppositional and adversarial, from mildly so to unbearable.  However, when most of the work of learning is handed over to students, when performance happens only as they feel ready and at low risk, when acts of learning are full of interesting, varied experiences and fun, when learning happens within a really functional community of interacting,supportive peers, when every stage is completed so that students are fully competent to move on to the next, and when many or most things to learn are self-chosen, students become almost driven to work hard, and for their own reasons.  Result:  they learn like clappers.  We all know it when we see it.  It’s what teachers live for.  

There are several sticking points on the way to achieving this, and then homework becomes almost a non-issue.  One is the absolute refusal of the system to give up some control, especially over timing.  The system overall has never paid anything but mealy-mouthed lip service to the part of our official Mission Statement that says people learn in different ways and at different rates.  We seem to say "Sure…yeah…but you still have to complete FOM10 in one semester, or X number of classes, or you FAIL, get no credit for learning anything, and have to start all over again."  "You have to move on to grade 6 now, and never mind all that grade 5 work you didn’t complete.  Good luck to you."

This leads to "squeaker passes" and the awful pattern of moving on to the next thing when not ready for it, and probably another fail.  It tells students in a loud voice that they don’t have to be really competent to "get out" of a year-grade or a course of study, and avoidance or disengagement has rewards (relief from stress, getting out of work they don’t want to do, elimination of risk, "sticking it to the man," declaring a pseudo-independence, status among peers, and more).  Remove these pernicious rewards, and their origins, and avoidance vanishes (perhaps after a short period of trying frantically to make it work again!).  Create an environment in which intrinsic rewards abound from genuine engagement, and they will come to the table.  If they engage learning it feels fabulous; if not….well…nothing.  And definitely not fabulous.  And no way out but another chance tomorrow to get ‘er done.  This is key:  we have to learn patience, and WAIT.

We have never just accepted that learning mathematics, for instance, is a  continuous process of acquiring knowledge and skills.  As a student, it just doesn’t matter to you what age-appropriate or development-appropriate peer group of fellow learners you are with this year, or where any of those kids are on the continuum, as long as you are somewhere on the continuum, moving steadily forward, and riding on a solid history of competence in all of the previous work.  We have to learn to trust kids to get there in their good time – with our help, of course. We have to let go of our insistence that every learner in a group must be nearly at the same place academically at any given time, and they all have to be doing the same thing at the same time, all day long.  

Step back a bit, and it looks as crazy as it really is.  Kids aren’t widgets and education is not mass manufacturing.  "Scientific management" was NEVER appropriate for schools, and never will be.  I am staggered by the human cost of this over the last two centuries, by the effects on millions of lives that we will never be able to guage fully, nor redeem.  Despite widespread, largely unfounded belief, it’s not even efficient.  In 2012, we know better, and yet we permit this one, tragically misguided set of notions about learning to dominate education worldwide to this day.

As competent, trained, experienced, caring adults, teachers do have the upper hand, but in many cases, we don’t use it as deftly as we could.  Observing where the real intrinsic rewards and natural consequences fall can be disturbing, but very helpful.  Interrupting the patterns of urging and resistance, of coercion and punishment, of risk and reward, means becoming very astute observers of what the school landscape feels like for students.  How can we change their view of school from jail-like institution to a resource-rich playground where the goodies are?

Piaget so rightly did advise us that play is, above all things, "the Great Work of children".  Play is hard work and results in rich, deep learning.  Children do not have to be forced to do it.  They are inwardly driven to play, and very inventive withal. Play is efficient, because it is child-selected, directed and timed; the energy and effort are focussed where they need to be, and exactly when. Maria Montessori proved how powerful this can be when we provide children with a truly rich environment, model civilized behaviour and true mentorship, and collaborate with children on their learning.  How can we transform ourselves from authoritarian keepers, lecturers and judges, to become preparers and guardians of rich learning environments, protectors, mentors, record-keepers, directors of traffic, facilitators and fellow-learners?  But that would mean reinventing our own identities somehow, and even adjusting our point of view, before we can transform learning in schools!

Another issue is our very difficult and uncomfortable relationship with the concept of evaluation.  Although we have all kinds of ways to determine whether a person can perform a skill or demonstrate knowledge at any number of levels of mastery (recognition, recall, application, synthesis, etc.), we are still collecting marks from early performance, or even formative stages, and averaging them with information from summative performance, sticking in some "credit" for what amounts to compliance or engagement attitudes, and claiming that this represents some kind of accurate picture of competence in a scope of challenges.  I have struggled with many iterations of this, none of them even in the ball park of real validity.  And none address the likelihood that skills may improve with time after instruction.

Many teachers do have a good grasp of the use of rubrics, checklists, and testing theory, and use them every day.  More and more are finding ways for students to demonstrate levels of mastery for summative evaluations that really do represent what students can do reliably and independently after learning and practice.  Too many of us are still wallowing in a miasma of mixed messages, imprecise language, unsupported beliefs, crossed wires, lack of guidance, administrative confusion and just plain muddleheadedness about what we’re really trying to do here.  And you can’t write comprehensive anecdotals on 150 kids every couple of months.  Get real.

The first thing is to admit that this is a much bigger, wholly systematic problem, and cannot be fixed with a few hints about marking or not marking homework.  We have work to do.  (Don’t we always?)  Psychologists speak of the "dances" of dysfunctionality, and admonish us that if we don’t like the dance we’re in, there’s only one way to move toward something better.  Each of us can only act individually; we can’t change others.  But if we change our own steps, we change the dance, and that can make all the difference.

When we do it together, we can change the world.

Oh, and in the short term, make a Big Deal of homework.  VALUE it.  Assign adjustable amounts of work (according to self-assessed need for gaining competence).  Assign tasks that are very high quality and meaningful.  Be sensitive to students’ need to have a life outside of school.  Teach students explicitly how to know when they can perform a task confidently and independently.  Set and insist on very high standards of work and presentation.  Talk about it, go over some of it in class.  Require completed, fully-documented corrections before checking off.  If it isn’t done right, it isn’t done.  Keep records.  Don’t count them, but show them to parents.  And there’s always after school.  On Friday. 😉

KT Pirquet

KT Pirquet is a professional writer/editor and retired high school mathematics and science teacher. Katie lives near Victoria, B.C., where she is currently a writing instructor at the Western Academy of Photography.

Doodling in Math Class with Vi Hart

 "If I am to have faults, I would rather they be my own." Vi Hart

 

Vi Hart is somewhat critical of math teachers in this video, and of systems which prevent exploration into mathematics in their desire to ensure that all students have equal exposure to mathematical ideas. Of course, as she points out, students rarely have exposure to mathematical ideas. Instead, what they usually experience are mathematical procedures to solve problems that aren’t their own.

Math in the real world: Train tracks

This is another in a series of posts about how one could find mathematics in the world around us.

Train tracks

My son loves to play with train tracks. A few days ago, while playing with his train tracks, he observed, "Daddy, I can’t turn a train around." I asked him what he meant. "No matter which way I go on this track, I can’t get my train to start facing in the other direction. I’d have to pick it up, but that’s cheating." (Note: I’m paraphrasing here)

Observations like this are mathematical observations about the world. He has abstracted from his train tracks to a property of his train tracks, specifically the direction his train is able to travel. He has then attempted, and I watched him do this, to verify this statement is true by running his trains around the track in every possible comination.

My wife and I spoke about this later, and she came to the observation that in order to be able to turn around his train on the track (without "cheating" by lifting it up), he needs a closed loop with a single entrance and exit point included in his track somewhere, and this entrance and exit point has to connect to the rest of the track in a certain way. So I asked the question, does he have the right track to be able to create a closed loop? If you look at the picture above, you may be able to answer this question yourself.

The area of mathematics that deals with these kinds of issues is called graph theory, and it was invented by Euler for a very different purpose many years ago. It is unfortunately not in most school curriculums, but it is certainly an interesting area of exploration, and one which is accessible to students.

They have call centres now

While I was at my mother’s house the phone rang so I picked it up.

"Hello?"

"Hello Sir," said a female voice on the other end of the line, with a slight accent, "We are calling you from an independent computer security company. We want to let you know that we have received numerous reports that your computer has downloaded viruses and malware, and we would like to help you fix your computer." In the background, I could hear the unmistakable background noise of a busy call centre.

"You know that’s impossible, right?" I responded.

"What’s impossible?" she responded.

"You can’t possibly, especialy as an independent computer company, know the phone number associated with a specific computer, even if you were somehow able to scan my mother’s computer remotely without her permission. You are trying to scam her. It won’t work this time. I teach people how to use their computers. I’ve taught my mother about you. You cannot scam my mother. I will record the phone call the next time you call, and forward it to Interpol. Leave my mother alone!" I said firmly. (I doubt Interpol would be able to do much about this scam, but hey, empty threats sometimes work.)

Click.

Warn your parents, your relatives, and anyone you care about who may be taken in by this scam. My mother got caught the first time, but with some help from me, we recovered her money, and I have hopefully helped immunize her from the scammers.

iPad apps for elementary school

We are introducing 30 iPads to our elementary school next year, and we are currently exploring what apps to put onto them. We have some suggestions as a place to get started, but I’ve been tasked with coming up with a list of useful apps for the iPads. I’m currently looking through my list of resources I’ve bookmarked for the iPad and deciding which of these apps I’ve seen will be most useful in our school’s context. (The screen-shots below are taken from the linked iTunes page).

  1. Move the Turtle

    Move the Turtle screen-shot

    This app both teaches kids how to use it (through a series of interactive puzzles) and allows students to create their own projects. It is based on the Logo programming language, but written using a sequence of commands chosen from the menu, rather than by typing. It works on the iPhone as well, but unfortunately (due to an issue with the Apple TOC) programs created with it cannot be shared.
     

  2. Tinkerbox

    Tinkerbox screen-shot

    This app allows students to build equipment to try and solve puzzles (which are based on physics concepts). I’ve not tried it out myself, but it is free, and so I’m going to at least try it out with the students.
     

  3. Show Me

    Show Me app

    This app allows students to draw and record their voice while drawing, letting them create a voice-over narration. It could be used for student created tutorials, stories, and animations. According to the description of this app, the videos created can be uploaded and shared via the ShowMe.com website.
     

  4. Motion Math

    Motion Math screen-shot

    The series of apps Motion Math makes for the iPhone and iPad are excellent, because they are more than just the typical flash card apps that are all too common in the app store for math. I’ve played with the fraction one myself (so has my son) and enjoyed using it, and seeing how it creates an alternate representation of fractions. This representation is hardly sufficient for students to completely understand fractions, but I’m sure it helps.
     

  5. Sketchpad

    Sketchpad app

    I’ve not used this app myself, but it comes recommended from Trever Reeh. From conversations with the mathematics teachers who work with Sketchpad, and from my time spent using Geometer’s Sketchpad a few years ago, I’m pretty sure this app will be useful. On the app description page, they note that they have activities built into it, which is encouraging.
     

  6. DragonBox

    DragonBox screen-shot

    DragonBox is a puzzle-game which tries to teach algebraic reasoning. It replaces algebraic symbols with visual representations (which are still themselves an abstraction of some arithmetic concepts) and then allows students to manipulate the symbols to try and solve the puzzles, which are all equivalent to standard algebra problems. It has a PC version which runs in the browswer and I have tried out as well. This is not a flash app so students can practice algebra – this game will try and teach students.
     

  7. Shuttle Mission Math

    Shuttle Mission Math screen-shot

    I’ve not tried this puzzle-game out myself, but I have used the paper and pencil version of the types of puzzles presented in this game with my students, and I found them very useful. Through solving the puzzles, students will have to employ (and learn) algebraic reasoning skills, which are explicitly described on the support page for this game.
     

  8. Scribblenauts

    Scribblenauts screen-shot

    This game allows students to type in words, get presented with images that represent those words, and use the images to solve a puzzle presented. The students have an enormous amount of freedom in what words they choose, and what images result. My son has loved playing this game, and spends his time playing it constantly asking us how to spell words, which he seems to be able to (mostly) remember for the next time he wants that particular item. 

 

These are some of the apps I’m looking into. I’d also like further recommendations. I’m looking specifically for iPad apps which:

  1. Are not just skill practicing / flash card apps. There are thousands of these, so finding them is easy, should our teachers want to use them.
  2. I’m hoping to find apps which will actually help teach concepts, rather than just review existing concepts. I’d like this teaching to be of the non-explaining-type teaching style, and more of the discovery-it-yourself-inside-a-guided-framework style of teaching. I can find things like the Khan Academy for myself fairly easily, but finding apps which support our inquiry-based teaching program in our elementary school is a bit more of a challenge.